Theorem albii

Description: Inference adding universal quantifier to both sides of an equivalence. (Contributed by NM, 7-Aug-1994)

	Ref	Expression
Hypothesis	albii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	albii	⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		albii.1	⊢ ( 𝜑 ↔ 𝜓 )
2		albi	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 ) )
3	2 1	mpg	⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 )